Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#12604 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C2×D4 |
| commutator | C4 | C2×C4×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×C22⋊C8 |
| prime radical | C2×#41×C17 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
482 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(22,23)(24,33)(25,38)(26,40)(27,30)(28,32)(29,35)(31,42)(34,46)(36,50)(37,43)(39,45)(41,52)(44,51)(47,48)(49,53);(22,24,26,36,27,37,41,51,28,34,42,48,25,35,39,49)(23,29,31,44,30,33,45,47,32,43,40,53,38,46,52,50);(18,20,21,19)(24,34)(29,43)(33,46)(35,37)(36,48)(44,53)(47,50)(49,51)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5592);